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Comment by TGower | Hacker News Reader

Dissapointing that the paper is full of simplifying, and seemingly unreasonable, assumptions instead of simulation based on the known orbital elements of all these tracked satellites. For example, collision cross section of 200 square meters when discussing starlink even though the satellites are about 4 x 3 meters. Assuming random distribution of trajectories. I'm also unconvinced that "how fast would a collision occur if all the electronics got fried" is a useful metric, in that scenario I'm much more worried about the situation on the ground and commercial avaition...

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Need to do a full read in more depth but it looks like they used a collision cross section of A=300 m^2, which is a little conservative but not insane given that the current Starlink v2 mini has about 90-120 m^2 of total surface area on its solar arrays. [1] The solar arrays are the largest part of these spacecraft by far and what defines the “collideable” area. A combined hard-body radius of 2 x 120 = 240 is in the ballpark for starlink-on-starlink collisions.

However most of collisions of concern are going to be starlink-on-debris, which is back down at the 120 m^2 level. Starlink already self screens for collisions and uplinks the conjunction data messages over the optical intersatellite link backbone or over their global ground station network.

If they aren’t able to talk to their satellites regularly from somewhere, you’re right we have MUCH bigger things to worry about on the ground.

[1] https://spaceflightnow.com/2023/02/26/spacex-unveils-first-b...

And wouldn’t the solar panels have less cross section than the satellite bodies, so even an apparent collision might just be a very near miss? (Honest question, not rhetorical, could be I’m wrong)

This is confusing terminology in the field, but you generally talk about the cross sectional area in the plane of the conjunction (https://www.space-track.org/documents/SFS_Handbook_For_Opera...) to calculate the probability of collision.

It’s a conservative definition in the field. It’s generally defined as the hard body radius: take the smallest sphere centered at the center of mass that would entirely enclose the object, then use the maximum cross section of that sphere to define the potential “area” of the colliding object.

Maybe put more simply, it’s the worst case area size / orientation you could be looking at. So yes. Solar arrays have a narrow cross section from the side but looking at them head-on (which is the angle used for Pc calculations) they’ll be very large.

Shouldn't they try and take some kind of probabilistic average area, rather than worst-case? I assume this is a statistical analysis.

It depends on what you're going for.

Generally people really don't want collisions due to cascading effects, so they take the worst-case probability of collision found with bounding assumptions. Additionally, while often all these vehicles have active attitude (orientation) control, sometimes they go into safe mode and are spinning (often spin stabilized to point at the sun), so it will clear the entire potential radius while rotating.

Also how do you define the probabilistic average area for a space object that you don't know how it's control system works or what it's been commanded to do / point at. Yes we can make some pretty good assumptions for things like Starlink, but even those do take safemodes occasionally.

So It's an engineering judgement call on how to model it. It's hard to get a probabilistic average for attitude that you can confidently test and say is "right", it's a lot easier and conservative to take the worst-case upper-bound. That's at least not-wrong.

Worth adding that the actual collision avoidance manouevres Starlink (and other satellites with propulsion) makes are based on more conservative assumptions

The papers assumptions lead to the conclusion that with no manouevres, we'd see a catastrophic crash between two or more satellites in LEO within 2.8 days. To be on the safe side, Starlink did over 144000 in the first six months of the year (and based on historical doubling rate, will probably be doing 1000 per day by now)...

Yeah the solar array on Starlink is held perpendicular to the velocity vector, so the cross section relative to the colliding body will invariably be smaller than the worst case.

They do verify their analytical calculation using a N-body simulation, that's section 4.4

> We verify our analytic model against direct N-body conjunction simulations. Written in Python, the simulation code SatEvol propagates orbits using Keplerian orbital elements, and includes nodal and apsidal precession due to Earth’s J2 gravitational moment. [...] The N-body simulation code used in this paper is open source and can be found at https://github.com/norabolig/conjunctionSim.

The cross section isn't actually all that outrageous, it corresponds to a hardbody radius of 4.5 meters. Hardbody radius is equal to the sum of the radii of the two colliding bodies, so 2.25 meters - which seems about right for Starlink.

They did an n-body simulation based on the known Keplerian orbital elements. That's exactly what you're asking for, right?

Also, the formalism is the standard way astrophysicists understand collisions in gases or galaxies, and it works surprisingly well, especially when there are large numbers of "particles". There may be a few assumptions about the velocity distribution, but usually those are mild and only affect the results by less than an order of magnitude.

"N-body simulation" doesn't mean what it's normally taken to mean here.

And the colliding gasses models have the huge assumption of random/thermal motion. These satellites are in carefully designed orbits; they aren't going to magically thermalize if left unmonitored for three days.

Well, sure, they won't be thermally random, but they will be significantly perturbed from their nominal orbits, particularly at the lower orbital altitudes.

Solar flares cause atmospheric upwelling, so drag dramatically increases during a major solar flare. And the scenario envisioned in the paper is basically a Carrington-level event, so this effect would be extreme.

That's why I mentioned the assumption about the velocity distribution. Sure, the velocities aren't Maxwell-Boltzmann, but that doesn't matter too much for getting a sense of the scale of the issue. The way an astrophysicist thinks (I am one) is that if we make generous assumptions and it turns out to not be a problem, then it definitely isn't a problem. Here they have determined it might be a problem, so further study is warranted. It's also a scientist strategy to publish something slightly wrong to encourage more citations.

The current "carefully designed orbits" has a starlink sat doing a collision avoidance manuever every 1.8 minutes on average according to their filing for December 1 to May 31 of this year.

Interestingly, the report from which they draw that number is one of the few that they cite but do not link to. Here's a link:

https://www.scribd.com/document/883045105/SpaceX-Gen1-Gen2-S...

It also notes that the collision odds on which SpaceX triggers such maneuvers is 333 times more conservative than the industry standard. Were that not the case (and they were just using the standard criterion) one might naively assume that they would only be doing a maneuver every ten hours or so. But collision probabilities are not linear, they follow a power law distribution so in actuality they would only be doing such maneuvers every few days.

It is disingenuous to the point of dishonesty to use SpaceX's abundance of caution (or possibly braggadocios operational flex) as evidence that the risk is greater than it actually is.

Agreed. This reads more like a hit-piece than a good-faith effort to quantify the risks. They make long-tail pessimistic assumptions, explicitly ignore possible mitigating factors, and act as if this "worse than worst case" scenario is a reasonable description of the world we live in.

Even the title "Orbital House of Cards" is unnecessarily editorializing.

  >we introduce the Collision Realization And Substantial Harm (CRASH) Clock

The needless forced backronym is another clue. It's Cargo Cult technical writing.

Why did this need to be a (badly done) acronym at all? It's a countdown to a collision, a collision clock, but of course "crash" (in all caps no less) sounds worse, and science writing needs sciencey acronyms don't ya know...

200 might be more reasonable for the next gen Starlink satellites.

Yeah they seem to have gotten excited to do the probability math (with bad assumptions, conflating a 300m^2(!) cross section collision with an actual probable collision), and with no consideration that this can actually be trivially simulated.

Also, if a solar storm actually wiped out all satellites in LEO (a huge assumption), who really cares how long it takes them to collide? Realistically it's all dead space until they de-orbit in a couple years.

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